Solid-state inertial sensor on chip

ABSTRACT

Monolithic solid-state inertial sensor. The sensor detects rotation rate about three orthogonal axes and includes a micromachined monolithic piezoelectric crystalline structure including an equal number of vibratory drive and detection tines on each side of an axis of symmetry of the sensor, the tines being synchronized to have alternate actuation movements inward and outward.

This application claims priority to U.S. provisional application Ser.No. 61/089,170 filed on Aug. 15, 2008, the contents of which areincorporated herein by reference.

BACKGROUND OF THE INVENTION

This invention relates to a solid state sensor element that combinesgyroscopic sensor function on three orthogonal axes with accelerometerfunction on three orthogonal axes, and more particularly to an inertialsensor using vibrating and torsion beams of a piezoelectric material.

Inertial sensors are used in various applications where progression ofthe movements, either linear or rotary, is not referred to an externalcoordinate system. These movements can be measured by gyroscopes andaccelerometers. In the past, such inertial sensors were used almostexclusively in navigation systems. In recent years, there has been agrowing interest in industrial applications of inertial systems inrobotic, automotive and, more generally, in the consumer market forconsumer electronics such as cell phones, digital cameras and portableGPS systems. Such inertial sensors represent an important component offuture human-machine interfaces as a lot of inertial information can beretrieved from an acceleration measurement by single and doublemathematical integrations to obtain the change in speed and position.With the rapid evolution of electronic components integration, suchinertial sensors are becoming smaller and cheaper but many technologycompromises are required to limit their costs. Nowadays, the physicaldimensions of a three axis gyroscopic solution remain large.

For more than 10 years now, the usage of micro-vibrating resonatorelements, as illustrated in FIG. 1, which generate out-of-planevibration when rotated around a sensitive axis is well established forvarious inertial applications in these markets, namely for inertialmeasurement units, inertial navigation or attitude and heading controlsystems. Similarly, many examples of accelerometers using vibratingelements are known from the prior art. For these inertial sensors,various types of materials can be used which are related to the type ofexcitation selected. If an external mode of vibration is selected, anon-piezoelectric material is normally used for the sensor element andthe drive vibration is mostly generated by electrostatic means. It isknown that such mode of excitation requires a high level of attentionregarding the package sealing as a minimal leakage would lead to a rapiddegradation of sensitivity.

For more than 40 years, it is established that high Q value crystallinequartz with a low level of dislocation represents a perfect choice toeliminate an hysterisis issue on micro-vibrating structures. Thebehavior of this piezo material is well described in the literature. Theelectronics associated with such a QMEMS device remains simple whichenables the possibility of a compact, low power requirement and areliable inertial system on a chip. Analog and digital signal outputsare directly retrieved from such QMEMS resonators.

On the inertial sensor market, there is a real need for a compact andaffordable sensor on a chip that combines gyroscope and linearaccelerometer functions on three axes of rotation and three axes oflinear displacement. These two functions are essential for inertialnavigation systems for military purposes, active suspension, chassiscontrol and braking systems in automotive, for monitoring during deepwells drilling among other inertial applications. On today's inertialsensor market, such combined functions are mostly realized by theaddition of a plurality of single axis sensors, which are gyroscopes andaccelerometers, linked to a common electronic platform. That duplicationof sensors has an impact on the size and the cost of the inertial sensorsolution.

It is well known that most of the manufacturers using inertial sensorsystems are looking to merge such independent sensors into a single,more compact and more affordable sensor system. In order to cope withthese on-going sensor clusterisation programs, it is the purpose of thepresent invention to merge three single axis gyro elements and threesingle axis linear accelerometer elements into one compact single solidstate sensor element that could be easily surface mounted on anelectronic assembly.

It is also an object of the present invention to propose a combinedsensor element that would be resistant to harsh environments from deepwells drilling in the oil industry or under hood conditions in theautomotive industry.

It is one of the objectives of the present invention to disclose anintegrated sensor element that can be easily manufactured with minimalsteps of operation using well known techniques, from affordablematerials. With the present invention, it is also possible to adjustfrequencies of vibrating forks and beams included in the gyro andaccelerometer portions.

Globally, it is an object of this invention to provide the largeelectronics market with a compact three axis gyroscope sensor combinedwith a three axis linear accelerometer sensor which can be easilymanufactured at low cost offering a tuning possibility as well as analogand digital output from simple drive and sensing electronics whileproviding long term stability and reliability for harsh environments.

SUMMARY OF THE INVENTION

In one aspect, the monolithic solid-state inertial sensor disclosedherein for detection of rotation rate about three orthogonal axesincludes a micromachined monolithic piezoelectric crystalline structureincluding an equal number of vibratory drive and detection tines on eachside of an axis of symmetry of the sensor, the tines being synchronizedto have alternative actuation movements inward and outward. In apreferred embodiment, the sensor further includes two pairs of vibratoryelements separated by a 60 degrees angle on each side of the axis ofsymmetry so that each pair of vibratory elements includes one vibratingtuning tine and one detection tine parallel to each other and linked bya common base.

It is preferred that the sensor include a trench in a central portioncreating a left and right side supporting the vibratory sensors. Thisembodiment may include six detection tines coupled at resonancefrequency to four parallel drive tines for detection of out-of-planevibration due to rotation around any axis of rotation. The sensor mayundergo a waving effect from left to right when rotated about a Y-axisto create a maximal electrical signal from detection tines on each sideof the trench. There may also be a waving effect from front to back whenrotated about an X-axis.

In yet another aspect, the invention is a monolithic solid-stateinertial sensor having independent gyroscope function on threeorthogonal axes of rotation and an accelerometer function on threeorthogonal axes of linear displacement. In one embodiment, theaccelerometer function is provided by a torsion bar and four vibratingbeam accelerometers, each one having an independent proof mass, aconnection arm, a pivot point to allow movement of the connection armalong a sensitive axis, and a vibrating beam attached at a selecteddistance from the pivot point.

In yet another aspect, the piezoelectric sensor includes detectioncircuitry having six detection tines sensitive to orthogonal vibrationmodes following an XY plane or YX plane plus electronic circuitryallowing a discrimination of vibration modes along the XY plane or YZplane and their amplitude which is proportional to the rate of rotationalong sensitive axes.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a perspective view of a prior art, single axis tuning forkgyroscope.

FIG. 2 is a perspective view of a prior art single axis vibrating beamaccelerometer (VBA) with independent proof mass.

FIG. 3 is an illustration of the reference axis used in the presentinvention.

FIG. 4 is a graph showing efficiency of the vibratory drive functiondisclosed herein to generate out-of-plane vibration for axes of rotationbetween 0 and 360 degrees.

FIG. 5 is a plan view of the gyroscopic sensor disclosed herein.

FIG. 6 is an isometric view of the gyroscope disclosed herein along withdeposited electrodes.

FIG. 7 is a plan view of an embodiment of a vibrating beam accelerometerdisclosed herein.

FIG. 8 is a perspective view showing more detail of the electroniccircuitry for a gyroscope portion.

FIG. 9 is a plan view showing a double butterfly arrangement for anembodiment of the invention.

FIG. 10 illustrates the behavior of detection tines when rotated aroundorthogonal axes.

FIG. 11 is a free body diagram for a vibrating beam accelerometer.

FIG. 12 is a cross-sectional view indicating the converse piezoelectriceffect in the driving forks of the gyroscope portion of the sensor.

FIG. 13 a is a cross-sectional view of the sensor showing the directpiezoelectric effect in the detecting forks of the gyro portion duringin-plane and out-of-plane vibration.

FIG. 13 b is a cross-sectional view illustrating the directpiezoelectric effect in a torsion bar of the accelerometer portion.

FIG. 14 a is a graph showing typical induced charges in detection tinesfor vibration modes 2 and 3.

FIG. 14 b is a graph illustrating frequency change as a function ofacceleration.

FIG. 15 is a flow diagram illustrating an embodiment of a manufacturingprocess for making the inertial sensor disclosed herein.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention relates to the juxtaposition of a three axisvibratory gyroscope and a three axis linear accelerometer in a robustsolid state design with high degree of freedom and sensitivity that iseasily integrated in a single chip element via a compact QMEMS designand simple electronics.

An innovation of this invention resides in a four wings butterflygyroscope using four vibrating forks as driving elements to generatelarge in plane vibration that are symmetrically disposed around rotationaxes X and Y. This drive vibratory mode is actuated by the conversepiezoelectric effect. Referring to FIGS. 3, 5 and 6, these driving forksare separated by 60 degrees and are substantially perpendicular to twoof the electrical axes. They are attached to a common base separated intwo portions by a trench parallel to the Y axis allowing moreflexibility of the base for the waving effect. A single detection tineis disposed parallel to each drive tine to measure the out of planevibration generated when the sensor is rotated around an X or Y axis.Two additional detection tines perpendicular to the third electricalaxis which is parallel to X are used to measure the in plane vibrationgenerated when the sensor is rotated around the Z axis.

The gyroscopic sensing function uses the direct piezoelectric effectfrom linear strains on detection tines created by the Coriolis forcegenerated when the sensor is rotated. The resulting pattern of voltagescaptured by the sensing electrodes is directly proportional to the rateof rotation around axis of rotation X, Y or Z. As indicated in FIG. 4,due to the direction of the drive actuation, the combined voltagesignals captured from group of tines 1-2 and 3-4 are maximal when thesensor is rotated around Y and progressively decreases to 0 when theaxis of rotation is progressively changed toward X. Inversely, thecombined voltage signals captured from group of tines 1-3 and 2-4 aremaximal when the sensor is rotated around X and progressively decreaseto a null value when the axis of rotation is progressively changedtoward Y.

In the present invention, a three axis accelerometer portion isintegrated in such a manner that no electrical interference ormechanical distortion is transmitted to the three axis gyro portion. Theaccelerometer portion is independent of the gyro portion; theaccelerometer portion has no effect on the performance of the gyroportion and inversely.

Referring to FIG. 7, the multi-axis accelerometer function is realisedby four VBA arrangements, each comprising a vibrating beam, a pivot, alever arm and a proof mass. Following X and Y axes, the differentiationof frequencies, obtained from opposite VBA arrangements, is proportionalto the acceleration along the sensitive axis. The accelerometer functionuses an independent torsion beam oriented along one of the electricalaxes and connected to the VBA arrangements 1 and 3. The directpiezoelectric effect is obtained from shear strains in this torsion barwhen the sensor is accelerated along the Z axis. The resulting inducedvoltage is directly proportional to the acceleration along this axis.

For the present invention, referring to U.S. Pat. No. 7,126,262 or U.S.Pat. No. 6,414,416, it is generally established that a vibrating forksdesign results in high Q due to the free ends and low energy loses, ifsome considerations are taken into account for the support design. Inthis invention, the in-plane inertial momentum is created withrelatively large tuning forks which are coupled to detection tines in aperfect symmetry to maximize the signal/noise ratio.

The piezo-electric properties and crystallography details of quartzmaterial are well described in a vast number of publications for thelast 40 years. It is established that a quartz crystal has a hexagonallattice with a 120 deg symmetry having three electrical axes X (a), asillustrated in FIG. 3. In the same plane, three mechanical axes Y areperpendicular to every electrical axis.

Generally speaking, Hooke's law provides a basic explanation for therelationship between elasticity and deformation. This law establishes arelationship between tension and displacement:

S _(i)=Σ(S _(ij) T _(j))

where i=1 to 6 represents the possible displacements which are eitherlinear displacements parallel to the main axis (j=1, 2, 3) orperpendicular (shear) to the main axis (j=4, 5, 6). Sij represents theelastic coefficients of the body, following each direction.

Similarly, the charge density of a piezoelectric material underconstraints is

$\begin{matrix}{{Q_{i} = {\sum\limits_{j = 1}^{6}( {d_{ij}\sigma_{j}} )}}{{i = 1},2,3}} & (1)\end{matrix}$

where Q represents the electric charge density in Coulombs, dijrepresents the piezoelectric coefficients and σ represents the appliedforce tension. For quartz and other trigonal class 32 piezo material,there are two independent piezoelectric factors organized following thiswell known matrix:

$\begin{matrix}\begin{pmatrix}d_{11} & {- d_{11}} & 0 & d_{14} & 0 & 0 \\0 & 0 & 0 & 0 & {- d_{14}} & {{- 2}d_{11}} \\0 & 0 & 0 & 0 & 0 & 0\end{pmatrix} & (2)\end{matrix}$

where rows represent a reference axis for the electric field orientation(X,Y,Z) while columns represent the surface orientation and straindirection which are respectively, from left to right, Xx, Yy, Zz, Yz orZy, Zx or Xz, Xy or Yx. The d₁₁ coefficient is established at 2.30×10⁻¹²mN (or C/N) and the d₁₄ coefficient is established at 0.6×10⁻¹² m/V.

The complete piezoelectric equation of a piezo sensor is:

$D = {{\sum\limits_{j = 1}^{6}( {d_{ij}\sigma_{j}} )} + {\sum\limits_{m = 1}^{3}( {ɛ_{m}E_{m}} )}}$

here ε_(m) represents the permittivity along X, Y or Z and E_(m)represents the electric field strength.

For the purpose of this invention, it is important to understand thebehavior of the quartz crystal in relation to these piezoelectriccoefficients and the induced charges on specific surfaces of the sensorcomponents.

The linear piezo coefficients from the first line of the matrix (2) arerelated to the drive and detection tines of the gyro and accelerometerportions. As illustrated in FIG. 13 a, electric charges in the Xdirection are created when linear strains occur on an X face, in the Xdirection and, inversely, on a Y face in the Y direction. Also in the Xdirection and following the right hand rule, smaller electric chargesare induced when shear strains occur in the Z direction on a Y face orwhen shears occur in the Y direction on a Z face.

The shear piezo coefficients from the second line of the matrix (2) arerelated to the torsion bars of the accelerometer portion. Significantelectric charges in the Y direction are induced, following the righthand rule, by shear strains in the X direction on a Y face or by shearstrains in the Y direction on an X face, as illustrated in FIG. 13 b.Smaller electric charges in the Y direction occur when shear strainsoccur in the Z direction on an X face or when shears occur in the Xdirection on a Z face. There is no other possibility of chargepolarization following the Y axis which provides a good insulation tomechanical noise due to other vibrating elements from the sensor.

The drive electrodes illustrated in FIG. 12 are connected to a regularsinusoidal oscillation circuit OS which is not detailed in the presentapplication. The frequency of this oscillation circuit is set to beequal to the natural frequency of the drive tines, which is 28.9 kHz forthe preferred embodiment.

From the first two piezo coefficients, d₁₁ and d₁₂ defined in matrix(2), it is established that an electrical field generated in the quartzcrystal in the +X direction will cause a contraction of the quartzcrystal in the Y direction. Inversely, an electrical field generated inthe −X direction will cause an expansion of the quartz crystal in the Ydirection. As explained in U.S. Pat. No. 6,675,651, it is known that,for a similar quartz cut, such compression and expansion occur maximallyat the surface around the electrodes area in the X direction.

Referring to FIG. 12 related to the drive circuitry, for the first halfsequence of the oscillation circuit, the electrodes 1,3,4,6,8 and 11 areconnected to a positive voltage while the electrodes 2,5,7,9,10 and 12are connected to a negative voltage. This pattern of connections isrepeated to the other drive tines arrangement.

Such voltage applied between these electrodes causes a resultantelectric field in the +X and −X directions inside the tuning forks, asillustrated by the arrows F1 to F4.

This resultant electric field creates a surface tension variation thatcauses the forks to bend in the +X or −X direction due to thecorresponding elongation or contraction in the Y direction. Inversely,as the piezoelectric effect is reversible, the induced potential isamplified and returned to the driving circuitry.

Referring to the FIG. 13 a, which is related to an example of detectioncircuitry of the gyroscopic function for the detection of in plane andout of plane vibrations, two patterns of charges are illustrated,depending of the induced strains in the detection tine.

When a detecting tine is coupled to an out-of-plane vibration (YZplane), a voltage proportional to the strain in the Y direction isobtained on the X faces from the piezo coefficient d₁₂, defined inmatrix (2). When the tine is forced down, a tension in the Y directionis induced at the upper portion (+Z) and a compression is induced at thelower portion (−Z). Consequently, positive charges appear on the −X faceof the detection tine at the lower portion level and on the +X face atthe upper portion level. When the detecting tine is forced up, theinverse electric pattern is induced on the −X and +X face, creating aninversion of the signal.

Similarly, when a detection tine is coupled to an in-plane vibration (XYplane), a voltage proportional to the strain in the Y direction isobtained on an X face from the same piezo coefficient. When thedetection tine is forced in the −X direction, the entire +X face of thedetection tine is under tension in the Y direction while the −X face isunder compression in the Y direction. Consequently, positive charges,relatively equally distributed, appear on both the X faces of thedetection tine. Consecutively, when the detection tine is forced in the+X direction, the entire +X face of the detection tine is undercompression in the Y direction while the −X face is under tension in theY direction. Consequently, no positive charges are generatedsimultaneously on both X faces of the detection tine.

To pickup the charges accumulated following the out-of-plane vibration(YZ plane) and in-plane vibration (XY plane), electrodes are sputteredonto the surface of the detection tines.

Referring to the FIG. 13 b, which is related to the detection circuitryof the accelerometer portion along the Z direction, one torsion barperpendicular to the Y axis is micro-machined and attached to two proofmasses using connection arms. Two patterns of charges are illustrateddepending of the direction of the acceleration. When the sensorexperiences an acceleration along the +Z direction, electric charges aregenerated on the Y faces of the torsion beam along the X axis. To pickupthese charges on the Y faces of the torsion bars, electrodes aresputtered on the YZ surfaces of the beam t, which is parallel to the Xaxis.

By definition, the main characteristic of a gyroscopic device is theability of its rotating or vibrating system to remain in the same planeas it is rotated. Physically, this in-plane inertia when rotated createsan orthogonal force that is proportional to the weight and the vibratingspeed of the drive elements as well as the rate of rotation. In thissensor, this resulting force, which is often called Coriolis force,creates a second or a third vibration mode which can be directlymeasured by sensing elements.

It is demonstrated in the literature that this vectorial force isdirectly proportional to the rate of rotation and can be described witha simple basic equation. Given that Coriolis acceleration (a_(c)) of avibrating tine as it rotates is:

a _(c)=−2(υ×Ω)

where υ represents the vibrating speed of the drive time and Ω theangular rate of the rotation movement.

The vibrating speed of the drive tine is related to the drive frequencyω. At a given time t, the in-plane position P_(x) of the vibrating tineis:

P _(x) =A sin(ωt)

where A represents the amplitude, under the condition of constantresonant frequency which is around 0.5 nm for the present invention.Along the same axis, the speed Vx of the vibrating tine is thederivative of the position:

V _(x) =dP _(x) /dx

V _(x) =Aω cos(ωt)  (3)

The Coriolis force (vector) applied on each drive tine as it is rotatedis F=ma_(c), where m represents the suspended mass of the vibrating tinearrangement.

Combining both functions, the Coriolis force (vector) on driving forksof the gyro portion when rotated around a corresponding sensitive axisis

Fc=−=−2mΩAω cos(w t)

This force is approximately 100,000 times weaker than the gravitationalacceleration.

Using FIGS. 5 and 6 as reference, this invention uses a butterflyarrangement of driving and sensing tuning forks having a 60 degreesymmetry, on each side of a central core which is separated by a trenchparallel to the Y axis. Incidentally, a total of four tuning forks arepresent; two on each side of the Y axis. Four detection forks parallelto the four driving tines are attached to the core just beside each ofthe driving tines. The configuration is symmetrical around X and aroundY. This amplitude is adjusted with the drive current to a maximum of 50nm, depending on the application and the desired range of rotation rate.In this design, it is important to establish the natural resonantfrequency ω of the driving forks arrangement as well as the currentgenerated by the detection forks as a function of the Coriolis force.

Incidentally, the Coriolis force (3) is generated when the vibratorydriving forks at resonant frequency are rotated along a sensitive axis.This force is orthogonal to the vibration direction and the rotationaxis. This force is transmitted from the base of the drive tines to thedetection tines and its action decreases by a factor (L−y) from the baseto the end of the detection beam. The tension (or compression) in the ydirection along the side of the detection tine is proportional to theamount of electric charges that can be picked up by the electrodes, asexplained in the previous section.

From Hooke's spring model, we have a relation between this constantCoriolis force and the associated bending displacement (u).

F _(c) =ku  (4)

where k represents the spring factor of the tuning fork which isresolved by an Euler-Bernoulli beam equation at equilibrium with amoment M=F_(c)(L−y), at a distance x from the side of the beam

$\begin{matrix}{\sigma_{y} = {\frac{{xF}_{c}( {L - y} )}{l} = {x\; E\frac{\partial^{2}u}{\partial y^{2}}}}} & (5)\end{matrix}$

where E is the Young's modulus for Alpha Quartz (in N/m²): 7.87×10¹⁰ andI is the moment of inertia of the rectangular shaped detection tines,which is

$I = \frac{t^{3}w}{12}$

With successive integration of (5) and terms simplification, we have

$\begin{matrix}{{u(y)} = \frac{2F_{c}{y^{2}( {{3L} - y} )}}{{Ewt}^{3}}} & (6)\end{matrix}$

From (6), the maximal displacement u, at y=L is retrieved,

$\begin{matrix}{{u(L)} = {\frac{4F_{c}}{Ew}( {L/t} )^{3}}} & (7)\end{matrix}$

Using (7) in (4), the spring constant of the detection fork, for amaximal displacement is retrieved,

$\begin{matrix}{k = {\frac{Ew}{4}( {t/L} )^{3}}} & (8)\end{matrix}$

Using this spring constant, the natural harmonic frequency of the driveand detection forks is retrieved

$\begin{matrix}{\omega = {\frac{1}{2¶}\sqrt{k/m}}} & (9)\end{matrix}$

where m is the mass of the vibrating forks. Using ρ=2650 Kg/m² for themass density of alpha quartz material, after substitution of (8) in (9)and simplification of the terms, the natural resonant frequency of thedriving forks is:

$\begin{matrix}{\omega = {c\frac{t}{2¶\; L^{2}}\sqrt{E/\rho}}} & (10)\end{matrix}$

where c is an adjustment factor for the vibration mode. With theproposed invention, the natural harmonic frequency of the driving forksis set at 28.9 kHz. The harmonic frequency of the detection forks is setto be slightly higher at 30.9 kHz.

Referring to the proceeding section and FIG. 8, the amount of electriccharges that can be picked up by the electrodes on the side of thedetection forks is a function of the tension (or compression) stresswhich is maximal at the YZ surface of the detection tines underdeflection in the YZ plane or XY plane due to the Coriolis force. Usingthe Euler Bernoulli beam equation (5), the charge density (inCoulomb/m²) which is a function of the Coriolis force Fc is

$Q = {{d_{11}\sigma_{y}} = {{d_{12}\sigma_{y}} = \frac{12\; d_{12}{F_{c}( {L - y} )}x}{{wt}^{3}}}}$

These electric charges are captured by electrodes and are maximal at y=0and x=t/2, respectively from the base and on the YZ surface (side) ofthe detection fork. Hence, the total current induced in two detectiontines, at every cycle of bending, from y=0 to y=L and from z=−w/2 tow/2, for x=t/2, is

P(x=t/2,y)=−2K¶f _(o) d ₁₂ F _(c)(L/t)²  (11)

which reduces to the following (in Coulomb/s=Amp)

${P( {x,y} )} = {2\lbrack {2¶\; f{\int_{z = {{- W}/2}}^{z - {W/2}}{\int_{y = 0}^{y = L}{\frac{12d_{12}F_{c}( {L - y} )x}{{Wt}^{3}}{y}{z}}}}} \rbrack}$

where K is a correction factor due to the limited area covered by theelectrodes on the side of the detection tines, which decreases theamount of charge collected. This relation is directly proportional tothe Coriolis Force which is proportional to the angular rate of rotation(3).

Referring to FIG. 5, the vibratory movement from the driving tines d1,d2, d3 and d4, in the XY plane, creates an orthogonal out-of-planevibratory mode as the structure is rotated around any axis between 0 to360 deg in the XY plane. For this invention, these out-of-planevibrations are called a second vibration mode. This second vibrationmode is captured by electrodes on detection tines s1 to s4 that arecoupled to the drive frequency. Incidentally, the induced charges aremaximal when these detection tines enter in resonance with the drivetines.

When a rotation occurs around the Z axis, an in-plane vibrationperpendicular to the direction of the vibratory drive tines, followingthe right hand rule of the Coriolis Force, is induced on the structure.This coupled in-plane vibration is called a third vibration mode.

These out-of-plane and in-plane vibrations are induced to the detectiontines through the central core of the gyroscope. As the tuning forksarrangements are suspended and because of the proximity of the naturalresonance frequency between the drive tines and the correspondingdetection tines, the vibration coupling from the base is easy, allowinggood sensitivity.

As explained in the preceding section, the rotation rate is directlyestablished by the amplitude measurement of the signal picked up by theelectrodes sputtered on the detection tines, which is proportional tothe rate of rotation. Also, as illustrated in FIG. 4, the strength ofthe induced charges is not the same for all detection tines, for a givenaxis of rotation, due to their respective orientation. The base ideabehind this butterfly design is to have a maximal signal from a group oftines when they are rotated around X and a null signal from the samegroup of tines when they are rotated around Y, and inversely.

As indicated in FIG. 4, due to the direction of the drive actuation, thecombined voltage signals captured from the group of tines 1-2 and 3-4are maximal when the sensor is rotated around Y and progressivelydecrease to zero when the axis of rotation is progressively changedtoward X. Inversely, the combined voltage signals captured from thegroup of tines 1-3 and 2-4 are maximal when the sensor is rotated aroundX and progressively decrease to a null value when the axis of rotationis progressively changed toward Y.

As indicated in FIG. 5, all drive tines are vibrating toward the samedirection, alternatively inward and outward, in order to create a wavingeffect in the structure as it is rotated. The resulting movements of thedetection tines are described in FIG. 10. Incidentally, when the sensoris rotated around Y, left tines are bending up while the right tines arebending down and inversely creating a waving effect of the structureparallel to the X direction. When the sensor is rotated around X, thetines at the back end, on each side of the sensor, are bending up whilethe tines at the front end, on the left and right side, are bending downcreating a waving effect parallel to the Y direction.

Using FIG. 6, these waving effects are accentuated by the fact that atrench separates the central core of the gyroscope in two portionsallowing more flexibility of the structure.

It is clear that the signal to noise ratio is greatly improved ascharges from more than one single tine are combined providing a strongersignal when the sensor is rotated.

As illustrated in FIG. 13 a, the charges induced at the surface of thedetection tines have a different pattern for in-plane and out-of-planevibration due to the piezo coefficient matrix (2). For out-of-planevibration, left electrodes (Upper and Lower) and right electrodes (Upperand Lower) have a difference of electric potential due to thepolarisation at the surface of the YZ face of the detection tines. Forin-plane vibration, there is no potential between these electrodes asthey are all charged identically.

As indicated in FIG. 10, when the sensor is rotated around Z, thedirection of the Coriolis force on the detection tines s1 to s4,following the right hand rule, is parallel to the detection tines. Thisaction pulls the back end of the gyroscope element on one side while thefront end is pulled on the other side, parallel to the X axis. Thiscreates a vibration of the structure in the XY plane that is accentuatedby the two cut offs operated at the base of the gyro sensor. Detectiontines s5 and s6 are attached to the core of the gyro portion, on eachside of the central trench, parallel to the Y direction. These twodetection tines are perpendicular to the direction of the vibrationmovement due to a rotation around Z. Hence, the signal from these twotines is maximal when the sensor is rotated around Z.

For these second and third vibration modes, resulting charges betweenelectrodes on corresponding detection tines are proportional to the rateof rotation around sensitive axes X, Y and Z, as demonstrated in FIG. 14a.

It is one of the goals of the present invention to propose a monolithicsolid-state inertial sensor that includes accelerometer functioncombined with the gyroscopic function described in the precedingsection. Four vibrating beam accelerometers are included in thisinertial sensor design to measure acceleration in the sensitive axes X,Y and Z. The disposition of the four VBAs is illustrated in FIG. 7.

The accelerometer portion is totally independent from the gyro portionas the multiple vibrating beam accelerometers have no effect on theperformance of the gyro portion and inversely. Referring to FIG. 7, eachaccelerometer includes, for example, a vibrating beam a1, a connectionarm c1 attached to the sensor frame by a pivot p1, a proof mass m1 and atorsion beam t.

For this type of sensor, referring to U.S. Pat. No. 6,662,658, U.S. Pat.No. 6,595,054 and U.S. Pat. No. 4,658,175, a common proof mass attachedto independent vibrating beams creates noise and perturbation. To avoidthese problems, vibrating beams from the accelerometer portion of thisinvention are attached to independent proof masses.

The vibrating beam a1, for example, is a simple beam orientedperpendicularly to an electrical axis of the quartz sensor with anatural frequency around 32 kHz. For certain applications, such a simplevibrating beam can be replaced by a double ended tuning fork (DETF)arrangement to decrease the noise transmitted to the structure. Everysingle or double vibrating beam is piezoelectrically driven to theirnatural frequency and they are connected via a connection arm to anindependent proof mass. As illustrated in FIG. 11, the vibrating beam isat a distance L0 from the pivot point and distance L1 from the inertiacenter of the proof mass M. Distance L1 is minimally ten times longerthan distance L0. Due to this configuration, the connection arm acts asa lever arm of the second type which magnifies the longitudinal tensileor compressive stress on the vibrating beam when the mass m isaccelerated along a sensitive axis.

As demonstrated in French patent EP0331557A1, the proof masses supportedby independent connection bars are hinged by connection arms whichprovide mechanical resistance against motion perpendicular to thesensitive axis. Inversely, these connection arms provide much lessresistance to motion along the sensitive axis in the XY plane.Incidentally, referring to FIG. 7, every connection arm is aligned withthe centroid of the attached proof mass to avoid pressure on thevibrating beam when the acceleration occurs in a direction parallel tothe connection arm.

At the back end of the sensor, two connection arms are attached to atorsion beam, which is oriented along the electrical axis X,perpendicular to the mechanical axis Y. Hence, two proof masses providea torque effect to the torsion bar when the sensor is accelerated alongthe Z direction. As mentioned in the preceding section, a directpiezoelectric effect is due to this shear force. The orientation ofthese torsion bars provides natural insulation against noise due to theother tension or compression forces.

For this sensor, the acceleration measurement is performed on the samethree sensitive axes used for the gyro portion. Referring to FIG. 7, VBA1 and 3 are sensitive to acceleration along the axis X. VBA 2 and 4 aresensitive to acceleration along the Y axis. Acceleration along the Zaxis is measured by the charges induced in the torsion beam which isstressed by a shear strain from proof mass m1 and m3.

Incidentally, for this invention, the accelerometer function along thesensitive axes X and Y is determined by the frequency changes of twoopposite vibrating beam accelerometers.

From the well known Rayleigh equation, it is established that a forceF=m₁a applied on the vibrating beam along its vibrating axes has aninfluence on its vibrating frequency where m1 is the proof mass and ‘a’is the acceleration to be measured. The relation between theacceleration to be measured and the frequency change is as follows:

$\begin{matrix}{\frac{\nabla f}{f_{0}} = {\frac{f_{s} - f_{0}}{f_{0}} = \frac{{kL}^{2}m_{1}a}{{Ewt}^{3}}}} & (12)\end{matrix}$

where f₀ is the natural frequency of the vibrating beam and k is aconstant parameter related to the fixed-fixed boundary conditions of thevibrating beams (k=0.3).

The sensitivity per pressure unit applied on the vibrating beam of thepresent design is around 6 Hz/Pa and the typical frequency changes forvarious accelerations is illustrated in FIG. 14 b. For this sensor, thesensitivity of the acceleration following an axis is due to the relativeposition of the vibrating beam, the pivot, the lever arm and the proofmass.

In this invention, the accelerometer function uses two identicalassemblies arranged so that an input acceleration places one beam intension and one beam in compression (push-pull). The output signal isthen taken as the difference frequency. Because of this, the effects oftemperature variation, nonlinearities and aging have no influence on theperformance of the accelerometer function.

It is established that the tensile strength of quartz material isapproximately established at 50 Mpa which represents the limit of theaccelerometer portion at 10,000 G.

For this sensor, it is easy to remove either the gyroscope or theaccelerometer portion to satisfy various requirements. The size of thesensor can be decreased accordingly.

This combined three axis inertial sensor is preferably made from Z-cutwafer with a rotation of 2 deg to 5 deg around the X axis, made of highquality, low etch channel density and low inclusion densitypiezoelectric quartz material. It is established from prior art thatsuch cut improves quartz crystal stability of the resonant frequencyover a wide range of temperatures. Ideally, the present invention ischemically manufactured from 75 mm or 100 mm pure crystalline quartzwafers. Such material is suitable because of its excellent mechanicalproperties which eliminate the risk of hysterisis that has an affect onthe stability of the scale factor. Also, the effect of time on thepiezoelectric properties of this material is negligible. It is alsopossible to use other trigonal class 32 material such as galliumphosphate which has the same form of piezoelectric constant matrix, withdifferent values however.

Referring to FIG. 15, this sensor is primarily machined by a commonchemical etching technique known from precedent art. In order tomaintain high manufacturing efficiencies and maintain low risk ofrejection due to flaws or dimensional issues, a deep reactive ionetching technique (DRIE) can be used. A standard wet etching processusing ammonium bifluoride solution at standard concentration andtemperature can be used to increase the etching rapidity but with moredimensional variability. Incidentally, to satisfy one of the mainobjectives of the present invention, all vibrating beams and forks aredisposed in such manner to ease the chemical manufacturing. Cavities andcut-outs are large enough to avoid undesirable residues or shape fromthe etching process. Critical dimensions to ensure an adequateperformance of the sensor are limited to the dimensions (length andthickness) of the vibrating elements. All other dimensions have largertolerances in all directions. Plating of electrodes is made from a wellknown technique, from the successive layer deposition of chromium andpure gold.

Respectively for each vibratory drive tines arrangement of the gyroportion, the drive and detection electrodes are routed in parallelorientation on the base. Connections are made from largely separatedconnection pads disposed on one side of the sensor to avoid an electricshort circuit. Drive electrodes of the accelerometer are routed on theother side of the sensor to large connection pads which are also largelyseparated. Connections to the electronic circuitries can be made eitherby soldering or by contact.

To satisfy one of the main objectives of the present invention, as perdemonstrated in U.S. Pat. No. 6,698,292, the drive and detectionelements of the gyroscopic portion of the preferred embodiment aremanufactured following strict ratios of width and thickness. Suchcontrol is important to decrease the influence of the operatingtemperature on the general performance of the gyro function. It is oneof the preoccupations of the present invention to satisfy a large rangeof temperature during operation.

Hence, all vibrating elements in this sensor design have a ratioWidth/Thickness to be between 0.5 to 1.5.

The contents of all the patents and references mentioned herein areincorporated by reference in their entirety.

1. Monolithic solid-state inertial sensor for detection of rotation rateabout three orthogonal axes comprising: a micromachined monolithicpiezoelectric crystalline structure including an equal number ofvibratory drive and detection tines on each side of an axis of symmetryof the sensor, the tines being synchronized to have alternativeactuation movements inward and outward.
 2. The inertial sensor of claim1 further including two pairs of vibratory elements separated by a 60degrees angle on each side of the axis of symmetry, wherein each pair ofvibratory elements includes one vibrating tuning tine and one detectiontine parallel to each other and linked by a common base.
 3. The inertialsensor of claim 2 wherein the sensor includes a trench in a centralportion creating a left and right side supporting the vibratory sensors.4. The inertial sensor of claim 1 including six detection tines coupledat resonance frequency to four parallel drive tines for detection ofout-of-plane vibration due to rotation around any axis of rotation. 5.The inertial sensor of claim 3 wherein the sensor undergoes a wavingeffect from left to right when rotated about a Y-axis to create amaximal electrical signal from detection tines on each side of thetrench.
 6. The inertial sensor of claim 3 that has a waving effect fromthe front end to the back end when rotated around an X-axis according tothe direction of the actuation from drive elements to create a maximalelectrical signal from the group of tines from the back end and thefront end.
 7. Monolithic solid-state inertial sensor having independentgyroscope function on three orthogonal axes of rotation andaccelerometer function along three orthogonal axes of lineardisplacement comprising a torsion bar and four vibrating beamaccelerometers, each one having an independent proof mass, a connectionarm, a pivot point to allow movement of the connection arm along asensitive axis, and a vibrating beam.